60 lines
2.7 KiB
Markdown
60 lines
2.7 KiB
Markdown
---
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title: Graphs
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---
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## Graphs
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A graph is a data structure you can use to solve routing problems, such as "Are these two components connected?" and "What is the shortest path from point a to point b?"
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A graph consists of nodes and edges.
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A node (i.e. vertex) is an object in your graph.
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A node can contain information such as the name of the node and which edges it is attached to.
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An edge is a link that connects two nodes.
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The edge can contain information such as the weight of the edge.
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If two nodes are connected by an edge, they are neighbours (i.e. adjacent).
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Depending on the problem you can use either two-way (undirected) or one-way (directed) edges.
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If you have an undirected edge from a to b, there is also a way from b to a.
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If you have a directed edge from a to b, there is not necessarily a way from b to a (as this would require a separate directed edge from b to a, which may not exist).
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You can use graphs to formulate situations such as:
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* Geographical maps
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* Each city in your country is a node
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* If two cities are connected by a road there is an edge between them
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* Roads can be one- or two-way (both directed and undirected edges)
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* The weight can be the length of the road
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* Flow of water
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* Each floodgate is a node
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* Each canal is an edge
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* Water will only flow in one direction so the edges are directed
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* The weight can be the maximum water capacity of the flow
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Example: a graph that has as nodes the capitals of the Nordic countries, and as (undirected) edges the driving distance to the cities connected by a direct road.
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```
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. +---------+
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. |Reykjavik|
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. +---------+
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.
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.
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. 529 km +---------+ 1760 km +--------+
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. +------------+|Stockholm|+---------+|Helsinki|
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. | +---------+ +--------+
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. + +
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. +----+ 1991 km |
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. |Oslo|+-------------------------------------+
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. +----+
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. +----------+
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. |Copenhagen|
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. +----------+
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```
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#### More Information:
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<!-- Please add any articles you think might be helpful to read before writing the article -->
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[Wikipedia](https://en.wikipedia.org/wiki/Graph_(discrete_mathematics))
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<a href='https://github.com/freecodecamp/guides/tree/master/src/pages/algorithms/graph-algorithms/breadth-first-search/index.md' target='_blank' rel='nofollow'>Breadth First Search (BFS)</a>
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<a href='https://github.com/freecodecamp/guides/tree/master/src/pages/algorithms/graph-algorithms/depth-first-search/index.md' target='_blank' rel='nofollow'>Depth First Search (DFS)</a>
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